In the third book of a projected four-volume series--which may well become the definitive history of our national pastime--Seymour ( Baseball: The Golden Age ) writes of baseball as a people's game. Himself a former Brooklyn Dodgers batboy (circa 1927), the author looks first at the game as played by children on sandlots and in schools, boys' clubs and even reform schools, concluding--unsurprisingly--that even at its most ragtag, baseball is an important part of growing up American. He claims that playing the game often spurred the assimilation of young immigrants, although its effectiveness in reforming juvenile delinquents is more debatable. Seymour also weighs baseball's role at the college level, where nonstudents have often been recruited and even professional players have been hired, as well as considering adult versions of the sport--town teams, industrial leagues, semi-pro ball and baseball in the armed forces, which has spread the game worldwide. Impressively researched and delightful to read, this third installment of his opus is enlivened by Seymour's many wry asides. Photos not seen by PW . (Apr.)